열전도 (Heat Conduction)

여기서부터 입력이번 글에서는 Duhamel’s theorem (두하멜의 정리)에 대해 알아보겠습니다. 두하멜의 정리는 boundary condition이 주어진 편미분방정식을 풀 때 사용하기 좋은 정리입니다. 두하멜의 정리를 이용하면 시간 $t$에 의존하는 boundary condition이 주어질 때의 편미분방정식을 풀 수 있습니다. Duhamel’s theorem 써먹을 수 있게 유도하기 시간에 의존하는 nonhomogeneous boundary condition 을 갖고, 하나의 homogeneous boundary condition 을 갖는 영역 $R$에서 … Read more

Let’s solve a heat conduction problem.A slab, 0 ≤ x ≤ L, is initially at uniform temperature T0. For times t > 0,the boundary surface at x = 0 is maintained at constant temperature T0, and the boundary surface at x = L is maintained at a prescribed time-dependent temperature T = T0 cos ωt, … Read more

Let’s solve a heat conduction problem. A semi-infinite medium, 0 ≤ x < ∞, is initially at a uniform temperature T0. For times t > 0, the region is subjected to a prescribed heat flux at the boundary surface x = 0: −k ∂T ∂x = f0 = constant at x = 0 Obtain an … Read more

Let’s solve a heat conduction problem.A semi-infinite medium, x > 0, is initially at zero temperature. For times t > 0, the boundary surface at x = 0 is subjected to a periodically varying temperature f (t) as illustrated in Figure 7-5. Develop an expression for the temperature distribution in the medium at times (i) … Read more

Let’s solve a heat conduction problem.A solid cylinder, 0 ≤ r ≤ b, is initially at zero temperature. For times t > 0, the boundary condition at r = b is the convection condition given as ∂T /∂x + H T = f (t), where f (t) is a function of time. Obtain an expression … Read more

Let’s solve a heat conduction problem.A hollow sphere a ≤ r ≤ b is initially at temperature T = F (r). For times t > 0, the boundary surface at r = a is kept insulated, and the boundary at r = b dissipates heat by convection with convection coefficient h into a medium at … Read more

Let’s solve a heat conduction problem. A hemisphere 0 ≤ r ≤ b, 0 ≤ μ ≤ 1 is initially at temperature T = F (r, μ). For times t > 0, the boundary at the spherical surface r = b is maintained at zero temperature, and at the base μ = 0 is perfectly … Read more

Let’s solve a heat conduction problem. In a one-dimensional infinite medium, −∞ <x< ∞, initially, the region a<x<b is at a constant temperature T0, and everywhere outside this region is at zero temperature. Obtain an expression for the temperature distribution T(x, t) in the medium for times t > 0. Heat Conduction problem solving I … Read more

열전달(Heat Transfer) 문제풀이해보겠습니다. 이번에 풀려고 하는 문제는 아래와 같습니다. Obtain an expression for the steady-state temperature distribution $T(r,\phi)$ in a long, solid cylinder$ 0 \leq r\leq b, 0\leq \phi \leq 2\pi$ for the following boundary conditions: The boundary at $r = b$ is subjected to a prescribed temperature distribution $f (\phi)$. 열전달(Heat Transfer) 문제풀이 다시 … Read more

열전달(Heat Transfer) 문제풀이해보겠습니다. 이번에 풀려고 하는 문제는 아래와 같습니다. A long, hollow cylinder, $a \leq r \leq b$, is initially at a temperature of $T = F(r)$. For times $t > 0$ the boundaries at $r = a$ and $r = b$ are kept insulated. Obtain an expression for temperature distribution $T(r, t)$ in the … Read more